WEALTH, DISPOSABLE INCOME AND CONSUMPTION - Economics

The time-series properties of net income and the real interest rate
are investigated more formally using two popular tests for unit roots – the
ADF test advocated by Dickey and Fuller (1979) and Said and Dickey
(1984), and the non-parametric test proposed by Phillips and Perron (1988).
The test results are reported in Table 1 and are largely consistent with the
inferences made on the basis of Figures 1 and 2. The ADF test and the
Phillips-Perron (PP) test both fail to reject the null of a unit root in the log
of net income but convincingly reject this null in the case of its first difference.
This suggests that the trend in net income is indeed stochastic and
that the growth rate of net income is a stationary process.
Table 1
Tests for unit roots –
augmented Dickey-Fuller (ADF) and
Phillips-Perron (PP) tests
Variables ADF lags
Sample: 1956:03–1993:03
ADF
t–ratio
PP
t–ratio
5%
critical
log of net income 3 –1.66 –2.21 –3.43
Δ
log of net income 1 –6.45 –11.22 –3.43
real interest rate 2 –2.52 –5.32 –3.43
Note: All tests are conducted with a time trend included in the unit-root regression.
In the case of the ADF test, the number of lagged first differences
of the dependent variable to include on the right-hand side was
chosen following the selection procedure advocated by Hall (1989).
This involves sequentially reducing the number of lags included until
the t-statistic on the highest-order lag included is significantly different
from zero. The lag selection began with four lags and used a 10 per cent
level for the t-test. For the PP test, the number of lags used in the nonparametric
correction for serial dependence is set to the square root of
the number of observations used, following the suggestion of Andrews
(1991). The critical values for the ADF and PP statistics are the same
and are computed for the actual number of observations available,
based on the response surface estimates given in MacKinnon (1991).
11